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We suggest a justification for all time of the formal development of geometric optics, for a conservative, genuinely nonlinear, initial-boundary value problem, in case of BV data with compact support and function of slow variables.
We consider the exact controllability problem for a three-dimensional linear elastic thin plate, with thickness 2ε and a polygonal middle surface. Controls are imposed on the lateral surface and at the top and bottom of the plate. The asymptotic limit when ε→0 is computed. We obtain that the...
We consider a shell, when first the thickness approaches zero and then the middle surface becomes flat. As noted by P.G. Ciarlet, the limit displacement obtained in this fashion is different from the limit displacement obtained when the shell becomes a plate first. Indeed, the ‘membrane’ and...
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